Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

Description:

In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces.

Creator(s): Farmer, Matthew Ray
Creation Date: August 2011
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
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Publisher Info:
Publisher Name: University of North Texas
Publisher Info: Web: www.unt.edu
Place of Publication: Denton, Texas
Date(s):
  • Creation: August 2011
Description:

In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces.

Degree:
Discipline: Mathematics
Level: Doctoral
PublicationType: Doctoral Dissertation
Language(s):
Subject(s):
Keyword(s): Strong Choquet | Baire category | analysis | topology | game theory | Banach spaces
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • LOCAL-CONT-NO: farmer_matthew_ray
  • ARK: ark:/67531/metadc84202
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
Holder: Farmer, Matthew Ray
License: Copyright
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.